Congruum g : 800 <= g <= 899

Definition 1.

k²g=mn(m²-n²)
k, m, n, g in N (integer > 0)

Definition 2.

(x/z², y/z³) on elliptic curve Y²=X³-g²X
x, y, z in Z (integer)
X, Y in Q (rational)

X=mg/n, Y=kg²/n²

Type means,

1. m=i², n=j²
2. m=i², n=i²-j²
3. m=i²+j², n=i²
4. m=j², n=i²-j²
5. m=i²-j², n=j²

There are 34 congruum g : 800 <= g <= 899.
The solution of the following numbers are found.

821, 871, 894

The solution of the following numbers are not in the range of 1 <= i, j <= 32,767.

807, 815, 822, 823, 829, 831, 838, 839,
853, 862, 863, 877, 878, 886, 887, 893

Congruum g : 800 <= g <= 899

g	m	n	x	y	z	type	i	j
805	81	80	13041	233289	4	(2)	9	1
806	49	13	3038	161448	1	(2)	7	6
	1651225	1421784	1651225	1078997795	42	(4)	1753	1285
	3073009	229441	2476845254	122923357349520	479	(1)	1753	479
813	196	75	53116	11309914	5	(2)	14	11
814	37222201	35897400	37222201	60047268301	210	(2)	6101	1151
821	672419525	37429924	552056430025	409544713903279485	6118	(5)	26643	6118
830	8405	5041	6976150	14743837800	71	(3)	71	58
854	13225	10309	185150	49903560	13	(2)	115	54
861	2541	2500	2187801	578971701	50	(5)	71	50
866	361	72	156313	60558947	6	(2)	19	17
	433	289	374978	170989968	17	(3)	17	12
	5303809	2996352	2296549297	90810454453271	1224	(4)	2881	2303
	8300161	2307457	16600322	64969361856	73	(2)	2881	2448
	168922009	135606025	146286459794	33362602321497072	11645	(3) (2) (1)	11645 12997 12997	5772 5772 11645
869	475904	286225	413560576	6719132596176	535	(5)	873	535
870	169	121	147030	39358800	11	(1)	13	11
	466603201	284650080	466603201	7986321741601	572	(4)	27409	21601
871	13293316	12809241	11578478236	333151482583270	3579	(1)	3646	3579
879	3844	3481	3378876	2634705810	59	(1)	62	59
889	64	63	8128	129032	3	(2)	8	1
	346921	90000	308412769	5230813038353	300	(1) (5) (4)	589 661 661	300 300 589
	3757168	1798281	3340122352	169491226887836	1341	(5)	2357	1341
	206778352	144072009	183825954928	56535583262349268	12003	(5)	18731	12003
890	49	40	4361	166341	2	(2)	7	3
	729	640	64881	7913079	8	(4)	37	27
	19881	10201	17694090	63884449200	101	(1)	141	101
	251001	249001	223390890	420652626000	499	(1)	501	499
894	1401941	1380625	1253335254	7708089337992	1175	(3)	1175	146
895	229441	56169	205349695	2853126090100	237	(1)	479	237

• 1 <= ‚‡ <= 99
• 100 <= ‚‡ <= 199
• 200 <= ‚‡ <= 299
• 300 <= ‚‡ <= 399
• 400 <= ‚‡ <= 499
• 500 <= ‚‡ <= 599
• 600 <= ‚‡ <= 699
• 700 <= ‚‡ <= 799
• 800 <= ‚‡ <= 899
• 900 <= ‚‡ <= 999